It means that you have benefited from DNA that they passed on to you. Neanderthals were actually very smart in terms of evolution, such as use of tools and so forth. When people migrated out of Africa, they mated with the Neanderthals, and then when they moved east, they mated with the Denisovans, another extinct branch of our ancestry. Today, people from Asia carry DNA from both these groups and have benefited from both. Most people with European ancestry only carry Neanderthal DNA, not Denisovan. The only people on Earth who do not have either are sub-Saharan Africans.
There is some controversy about what benefits Neanderthal DNA has passed down to us, but some theorize that Neanderthal DNA has increased cognitive function in those who carry it, among other things.